Aircraft: CRJ200
Phase of flight: Cruise
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Maintenance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence

Late in our descent we got 'STAB TRIM' and 'MACH TRIM' status messages. I tried to re-engage the stabilizer trim and it immediately disengaged. I asked the First Officer/pilot flying to also work the radios while I ran the QRH checklist. As I neared the end of the 'MACH TRIM' QRH procedure we got an 'AP TRIM' message. I noticed the stab trim numbers decreasing so I took the controls and disconnected the autopilot. The plane was flying with very nose-down trim (I think it read 2.2 when I disconnected the autopilot). I told the First Officer to run the stab trim runaway immediate action items. I had begun the descent at this point and had declared an emergency. We were close to our destination so I planned to land there. ATC gave us direct to the airport; I made a PA and talked to the Flight Attendant while in the descent. The First Officer completed the QRH procedure and we were within five minutes of landing when ATC said that the airport was detecting windshear on the approaches. Shortly after that ATC said that the alert had cleared (or something to that affect) so we continued. On about a 5 mile final ATC said they were getting windshear detections again and that an Airbus that just landed reported a gain of 25 KTS. I called for the go-around and asked for a left turn away from what was starting to look like a rain shaft over the airport. ATC asked our intentions and I decided to divert to and land at another area airport. The malfunction and the weather were big threats. The plane took some work but was controllable and I don't think we deviated from our ATC cleared routes/altitudes. I made a few mistakes. I am not sure that I called for the correct checklist. I saw the stabilizer trim moving and when I disconnected the autopilot and felt how out of trim the plane was my first reaction was a runaway. In retrospect we might have looked at the QRH procedure for 'AP TRIM' first. I felt very busy throughout the whole mess and I never sent the Dispatcher a message saying we were diverting. I didn't forget; it was a conscious decision but looking back now I question it. When we got on the ground I got very busy trying to catch the Dispatcher up; coordinate a gate; accommodate the passengers and take care of my crew that it took me a long time to talk to Maintenance. The Maintenance Controller was obviously upset with me about being called so late in the process. When I spoke to the Dispatcher early on I asked if Maintenance knew what was going on and she had said that they were sitting right next to her and that the ball was already rolling. I intended to call them with specifics later but subconsciously I thought of them as 'notified'. I didn't call until a Scheduler reminded me to. That was a big mistake; I should have called them immediately. A CRJ-200 flight crew experienced stab/autopilot/mach trim pitch axis anomalies while on descent to their destination. Windshear and weather ultimately precluded their emergency landing at their destination and they diverted to another area airport not yet so affected. The heavy workload thus encountered precluded a timely contact with Maintenance.